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Simplifying x2 + -34x + 89 = 0 Reorder the terms: 89 + -34x + x2 = 0 Solving 89 + -34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-89' to each side of the equation. 89 + -34x + -89 + x2 = 0 + -89 Reorder the terms: 89 + -89 + -34x + x2 = 0 + -89 Combine like terms: 89 + -89 = 0 0 + -34x + x2 = 0 + -89 -34x + x2 = 0 + -89 Combine like terms: 0 + -89 = -89 -34x + x2 = -89 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = -89 + 289 Reorder the terms: 289 + -34x + x2 = -89 + 289 Combine like terms: -89 + 289 = 200 289 + -34x + x2 = 200 Factor a perfect square on the left side: (x + -17)(x + -17) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + -17) equal to 14.142135624 and -14.142135624.Subproblem 1
x + -17 = 14.142135624 Simplifying x + -17 = 14.142135624 Reorder the terms: -17 + x = 14.142135624 Solving -17 + x = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 14.142135624 + 17 Combine like terms: -17 + 17 = 0 0 + x = 14.142135624 + 17 x = 14.142135624 + 17 Combine like terms: 14.142135624 + 17 = 31.142135624 x = 31.142135624 Simplifying x = 31.142135624Subproblem 2
x + -17 = -14.142135624 Simplifying x + -17 = -14.142135624 Reorder the terms: -17 + x = -14.142135624 Solving -17 + x = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -14.142135624 + 17 Combine like terms: -17 + 17 = 0 0 + x = -14.142135624 + 17 x = -14.142135624 + 17 Combine like terms: -14.142135624 + 17 = 2.857864376 x = 2.857864376 Simplifying x = 2.857864376Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.142135624, 2.857864376}
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